III.2. Conditioning regimens The conditioning regimens used will be either the one developed in Seattle (TBI arm) or the one developed by the Stanford group (TLI arm). These 2 regimens have been extensively reported in major medical journals. In the TBI arm, conditioning will consist of fludarabine 30 mg/m2 on days -4, -3 and -2 (total dose 90 mg/m2), followed by a singe dose of 2 Gy TBI administered on day 0, at a low dose-rate (≈ 7 cGy/min), before infusion of cells. In the TLI arm, conditioning will consist of 8 Gy TLI and ATG. TLI will be administered by linear accelerator at a dose of 80 cGy daily, starting 11 days before transplantation, until a total of 10 doses (800 cGy) has been delivered. The irradiation will consist of a supradiaphragmatic mantle field, a subdiaphragmatic field including an inverted Y and splenic ports, encompassing all major lymphoid organs, including the thymus, spleen, and lymph nodes, as used in the treatment of Hodgkin's disease (Kaplan HS, Cancer Research 26:1268-1276, 1966). The Waldeyer ring is not included. ATG (Thymoglobulin®, Genzyme), at a dose of 1.5 mg/kg/d, will be given intravenously on days -11 through -7.